First Law of Black Saturn Thermodynamics

The physical version and equilibrium state version of the first law of thermodynamics for a black object consisting of n-dimensional charged stationary axisymmetric black hole surrounded by $a$ black rings, the so-called black Saturn was derived. The general setting for our derivation is n-dimensional dilaton gravity with p + 1 strength form fields.Comment: 9 pages, RevTex, to be published in Phys.Rev.D1

Covariance matrices of length power functionals of random geometric graphs -- an asymptotic analysis

Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process increases. This includes a systematic discussion of matrix properties like rank, definiteness, determinant, eigenspaces or decompositions of interest. For the formulation of the results a case distinction is necessary. Indeed, in the three possible regimes the respective covariance matrix is of quite different nature which leads to different statements. Finally, stochastic consequences for random geometric graphs are derived.Comment: 26 page

Higher dimensional abelian Chern-Simons theories and their link invariants

The role played by Deligne-Beilinson cohomology in establishing the relation between Chern-Simons theory and link invariants in dimensions higher than three is investigated. Deligne-Beilinson cohomology classes provide a natural abelian Chern-Simons action, non trivial only in dimensions $4l+3$, whose parameter $k$ is quantized. The generalized Wilson $(2l+1)$-loops are observables of the theory and their charges are quantized. The Chern-Simons action is then used to compute invariants for links of $(2l+1)$-loops, first on closed $(4l+3)$-manifolds through a novel geometric computation, then on $\mathbb{R}^{4l+3}$ through an unconventional field theoretic computation.Comment: 40 page

Topological Sectors of Spin 1 Theories} in 2+1 Dimensions}

It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically non-trivial regions of space-time. The partition function of these theories, when constructed on an arbitrary Riemannian manifold, differ by a topological factor, which is equal to the partition function of the pure Chern-Simons theory. This factor is related to the space of solutions of the field equations of the Topological Massive Theory for which the connection is asymptotically flat but not gauge equivalent to zero. A new covariant, first order, gauge action,which generalize the ``Self-dual'' action, is then proposed. It is obtained by sewing local self-dual theories. Its global equivalence to the Topological Massive gauge theory is shown.Comment: 11 page

Scaled metal forming experiments: A transport equation approach

The focus of this paper is on a method for the design of bespoke small-scale pilot, metal-forming processes and models that accurately represent corresponding industrial-scale processes. Introducing new complex metal forming processes in industry commonly involves a trial and error approach to ensure that the final product requirements are met. Detailed process modelling, analysis and small-scale feasibility trials could be carried out instead. A fundamental concern of scaled experiments, however, is whether the results obtained can be guaranteed to be representative of the associated industrial processes. Presently, this is not the case with classical approaches founded on dimensional analysis providing little direction for the design of scaled metal-forming experiments. The difficulty is that classical approaches often focus predominantly on constitutive equations (which indirectly represent micro-structural behaviour) and thus focus on aspects that invariably cannot be scaled. This paper introduces a new approach founded on scaled transport equations that describe the physics involved on a finite domain. The transport approach however focuses on physical quantities that do scale and thus provides a platform on which bulk behaviour is accurately represented across the length scales. The new approach is trialled and compared against numerically obtained results to reveal a new powerful technique for scaled experimentation

Notes on the Third Law of Thermodynamics.I

We analyze some aspects of the third law of thermodynamics. We first review both the entropic version (N) and the unattainability version (U) and the relation occurring between them. Then, we heuristically interpret (N) as a continuity boundary condition for thermodynamics at the boundary T=0 of the thermodynamic domain. On a rigorous mathematical footing, we discuss the third law both in Carath\'eodory's approach and in Gibbs' one. Carath\'eodory's approach is fundamental in order to understand the nature of the surface T=0. In fact, in this approach, under suitable mathematical conditions, T=0 appears as a leaf of the foliation of the thermodynamic manifold associated with the non-singular integrable Pfaffian form $\delta Q_{rev}$. Being a leaf, it cannot intersect any other leaf $S=$ const. of the foliation. We show that (N) is equivalent to the requirement that T=0 is a leaf. In Gibbs' approach, the peculiar nature of T=0 appears to be less evident because the existence of the entropy is a postulate; nevertheless, it is still possible to conclude that the lowest value of the entropy has to belong to the boundary of the convex set where the function is defined.Comment: 29 pages, 2 figures; RevTex fil

On Babylonian lavatories and sewers

This study begins by examining the archaeological and documentary evidence for lavatories (toilets) and foul-water drains in ancient Mesopotamian dwelling houses. It goes on to investigate the use, etymology and history of the Akkadian word asurrû: in the Old Babylonian period it served mainly as a term for a kind of foul-water drain or “sewer” but later shed that meaning

New Investigations in the Environment, History and Archaeology of the Iraqi Hilly Flanks: Shahrizor Survey Project 2009-2011

Recent palaeoenvironmental, historical, and archaeological investigations, primarily consisting of site reconnaissance, in the Shahrizor region within the province of Sulaymaniyah in Iraqi Kurdistan are bringing to light new information on the region’s social and socio-ecological development. This paper summarises two seasons of work by researchers from German, British, Dutch, and Iraqi-Kurdish institutions working in the survey region. Palaeoenvironmental data have determined that during the Pleistocene many terraces developed which came to be occupied by a number of the larger tell sites in the Holocene. In the sedimentary record, climatic and anthropogenic patterns are noticeable, and alluviation has affected the recovery of archaeological remains through site burial in places. Historical data show the Shahrizor shifting between periods of independence, either occupied by one regional state or several smaller entities, and periods that saw the plain’s incorporation within large empires, often in a border position. New archaeological investigations have provided insight into the importance of the region as a transit centre between Western Iran and northern and southern Mesopotamia, with clear material culture links recovered. Variations between periods’ settlement patterns and occupations are also beginning to emerge